Imagine
a low-resolution sensor. A higher-resolution sensor can be obtained by cutting
each pixel of the low-resolution sensor into four smaller pixels:

For
a given exposure time, each smaller pixel receives four times less light than a
large pixel—the equivalent of reducing exposure time by a factor of four. So to
get the same sensor response, exposure time needs to be multiplied by four,
which means that the ISO sensitivity of the high-resolution sensor is four
times less than the low-resolution sensor.

Now
assume that the same exposure times and identical ISO settings are used with a
low-resolution camera and with a high-resolution camera having four times as
many pixels. Since each high-resolution pixel is intrinsically less sensitive,
a higher gain (either analog or digital) is applied to the signal, yielding
more noise.

Let
I denote the gray level on the sensor, and sL(I ) and sH(I ) the standard deviation
on the low- and high-resolution sensors, respectively. With equivalent
technology, the high-resolution sensor has more noise because of the higher
gain: sL(I ) < sH(I ).

However,
the four high-resolution neighboring pixels can be averaged out to form a
low-resolution pixel. The statistical formula below shows the noise yield for
the downsampled image:

The
new SNR is

The
loss of resolution produces a better SNR. We now have two images at the same
resolution and shot in similar conditions. When printing with the same printer
using the same format, it is more relevant to compare sL(I ) and sH(I ) + 6dB.

Further readings for the Contrary to conventional wisdom, higher resolution actually compensates for noise

To provide photographers with a broader perspective about mobiles, lenses and cameras, here are links to articles, reviews, and analyses of photographic equipment produced by DxOMark, renown websites, magazines or blogs.

On DxOMark, we evaluate and rank many types of digital cameras with image sensors that vary widely in pixel count, pixel size, and digital signal processing. To ensure that sensor performance comparisons between cameras are fair, it is very important both to test under identical shooting conditions and to take viewing conditions into account.